I like the idea of rating the games separately; you could still have an overall score (counting only the games that the player has played). It would make sense to factor in the various game imbalances BUT since they're calculated on a sample of games, those numbers could be refined over a period of time, making earlier score calculations invalid.

nath wrote:Also variants with a lot of draws like 'old' Hnefatafl let look the distance between players much smaller than it looks with a draw-less variant like Copenhagen Hnefatafl.

There'll be less draws with 'old' Hnefatafl in future. 'Old' Hnefatafl and several other variants descend from the David Brown Hnefatafl, and it would be natural for them to inherit from this the win-by-surrounding-all-whites rule.

nath wrote:I would also suggest to give only a k-factor of 16 (the half) if the player played a basic amount of games (20 or 30).

The rating calculation can be improved especially for games against new players with unestablished ratings.

cyningstan wrote:It would make sense to factor in the various game imbalances BUT since they're calculated on a sample of games, those numbers could be refined over a period of time, making earlier score calculations invalid.

The game imbalances are already included in the rating calculations. The balance values are reasonably accurate, they're in most cases based on many hundreds of games and change but little.

The beauty of the Elo rating system is that your rating will at all times approach your "true" number, no matter where you start - like a pendulum which can oscillate but always finds back to its equilibrium. So if for one or the other reason a player's rating is too high or too low, it will correct itself through his next games anyway.

Last edited by Hagbard on Sun Feb 26, 2017 10:39 am, edited 1 time in total.

The main problem here is that you get a medium rating (no matter where you start) by participating in test tournaments and anyways your rating is totally flipped by just loosing a two games in a row against a player that have some difference to you (for example I lost 31 points against you in just one game). The Elo system is developed for chess (I play also chess). But the change of the rating is much slower than here (if the player has such a basic amount of games). The problem is that the rating change to quickly here.

In 'Old' Hnefatafl the king can't escape if you play against experienced players. I don't think that it is a good variant to rate. But also for reasonable variants I'd prefer different ratings. Copenhagen Hnefatafl and Sea Battle Tafl (9x9) are both good and interesting variants, but completely different. Since Copenhagen Hnefatafl is a game of developing pieces, Sea battle tafl is a game of fast tactical play. If I play Sea battle tafl my rating go down, if I play Copenhagen Hnefatafl my rating goes up. Why should a player that just catchs me in Sea battle tafl has a better rating than one that is a serious opponent in Copenhagen Hnefatafl for me? Different ratings are necessary.

I must admit that I personally like the joint overview of the total rating list very much. When you look through the list, all players are positioned absolutely reasonably.

But I'll work on this problem after New Year.

As for the test tournaments:
In some cases the balances of some variants were completely unknown, and those tournaments were not rated.
For the rated tournaments, the rating calculation is adjusted for game balance (reasonably known), and furthermore everyone plays two games of reverse colors against each opponent, so the risk is limited.

Hagbard, this will probably sound like a silly question, but in your figures for game balance, I believe "+1" represents perfect balance; my question is, does "-1" also represent perfect balance?

If so, the system skips any numbers between +1 and -1, so that subtracting 0.1 from 1 would give -1.1, and not +0.9. This strikes me as a bit odd.

If not, then a game balance of "-1" would be the same imbalance (in the other direction) as a game balance of "+3" (because it's 2 away from the ideal) - this also strikes me as a bit odd.

Sorry I'm not a mathematician so I'm struggling to understand this; it probably seems obvious to most people. My non-mathematical brain wants to see "zero" as the perfect game balance, with plus or minus representing bias in one direction or the other.

Yes, with this way of calculating, +1 is identical to -1, perfect balance.
When overweight flips from white to black, the sign flips from + to - and the fraction turns upside down.
Subtracting 0.1 from 1 gives -1.1.
A game balance of "-3" is the same imbalance (in the other direction) as a game balance of "+3".

The balances would be a continuous function, were instead shown the logarithm of the balance, but that would be impractical and hard to read.

crust wrote:My non-mathematical brain wants to see "zero" as the perfect game balance, with plus or minus representing bias in one direction or the other.

When a game variant seemingly is well balanced (game balance near 1), theoretically the fine balance can have another cause than the game working well.
Imagine some completely uncontrollable game, where the outcome is like throwing a dice. The "game balance" of such a game would be 1.

To find out if any of our variants is uncontrollable in this way, the game haphazardness was calculated as:
(number of games where, after adjusting for game balance, a lower rated player wins against a higher rated player) divided by (number of games). Draws are counted as half wins.The game haphazardness is the percentage of games where a weaker player beats a stronger player.

Example:
In Skalk Hnefatafl 11x11 (game balance -4.00), a white player rated 1740 against a black player rated 1500 both have the same chance of winning.
Thus if a white player rated 1700 beats the black player rated 1500, then the outcome is unexpected and counted.

In a completely uncontrollable game, where the outcome is random, the higher rated player would win half the games and lose half the games, and the game haphazardness would be 50%.
In a completely controllable game, where the higher rated player always wins, the game haphazardness would be 0 %.

At bottom of the list is a candidate for an example of the phenomenon of "good balance" caused by random outcome.
Tawlbwrdd Lewis cross 11x11 seems to have a fine balance of -1.11 but a haphazardness of 34.5%. When playing the game, it appears rather chaotic because of the eight open lines, in my opinion, and the chaos could be the reason for the balance.

Last edited by Hagbard on Sat May 13, 2017 6:00 pm, edited 2 times in total.

Nath wrote:maybe we should just make different ratings for each variants and display them in a different menu.
...
I would also suggest to give only a k-factor of 16 (the half) if the player played a basic amount of games.
Between Grandmasters in chess a k-factor about 10 is used.
We have to fast changes if just one or two games are lost.

Cyningstan wrote:It would make sense to factor in the various game imbalances BUT since they're calculated on a sample of games, those numbers could be refined over a period of time, making earlier score calculations invalid.

Rating and game balances.
Since July 2013 the game balances are recognised in rating calculations.
If the balance of a variant is not sufficiently accurately known, then the game is not rated.
Ex.: In Skalk Hnefatafl 11x11 (game balance -4.00) a white player rated 1740 against a black player rated 1500 both have the same chance of winning, and are therefore considered of equal strength in this case.

Rating and k-factor.
Since December 2013 the k-factor varies from 64 for newcomers to 12 for veterans.
Newcomers affect very little the ratings of established players (k-factor near 0).

Separate ratings per variant.
The following page shows rating lists for each variant plus the total. All the ratings are calculated from scratch using the newest game balance values.http://aagenielsen.dk/separate_ratings.php
The total ratings list built from scratch is by and large identical to the old rating list on the page "Play tafl against other tafl players".

Last edited by Hagbard on Sat May 13, 2017 5:59 pm, edited 2 times in total.